局部可实现单元操作的局部标记
Local Marking of Locally Implementable Unitary Operations
AI总结：
研究局部可实现单元操作的局部标记任务，展示了一组无法通过局部操作标记的三粒子产品单元操作，揭示了标记与区分之间的差异。
摘要：
我们研究了局部可实现单元操作的局部标记任务。在这种设定中，从已知集合中随机选择的多粒子量子单元通道被分配给空间上分离的各方，而不暴露其身份。目标是仅使用局部操作和经典通信（LOCC）正确识别（标记）所应用的过程。虽然局部可区分性意味着局部标记，但局部标记并不保证单元操作的局部或全局可区分性。因此，标记任务不等同于区分任务。我们通过构造一组全局可区分的三粒子产品单元操作，展示了非局域性无纠缠的更强表现，这些操作无法通过局部标记。与状态标记不同，我们发现对产品单元操作子集进行标记并不意味着能够标记更大的子集。最后，我们探讨了在局部标记背景下，相对于标准区分场景，探测器-纠缠和产品之间的层次结构。
英文摘要：
We investigate the task of local marking for locally implementable unitary operations. In this setting, multipartite quantum unitary channels, chosen randomly from a known set, are distributed among spatially separated parties without revealing their identities. The objective is to correctly identify (mark) the applied process using only local operations supplemented with classical communication (LOCC). While local distinguishability implies local marking, local marking does not guarantee either local or even global distinguishability of a set of unitaries. Thus the task of marking is not equivalent to the task of discrimination. We demonstrate a stronger manifestation of nonlocality without entanglement by constructing a set of globally distinguishable tripartite product unitaries that cannot be locally marked. In contrast to state marking, we find that marking a subset of product unitaries does not imply the ability to mark a larger subset. Finally, we explore the hierarchy of probes-entangled and product-in the context of local marking with respect to the standard discrimination scenario.
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